Question

 

Can someone help me & please give me the answers to these 5 problems? 1.) If f(x)=3x+9 , what is f-1(x)?  A: f-1(x)=1/3x-3  B: f-1(x)=-1/3x-9 C: f-1(x)=-3x-9 D: ff-1(x)=1/3x+9 2.) If f(x)=3/x and g(x)=3x , which of the following statements is true?  A: (f · g)(2)=2  B: (g · f)(2)=0 C: (f · g)(9)=1 D: (g · f)(-9)=-1 3.) If f(x) and g(x) are inverse functions or each other, which of the following statements is true?  A: f(x)/g(x)=1  B: f(x)=-g(x) C: (f · g)(x)=1 D: (g · f)(x)=x 4.) If f(x)=4x-2 and g(x)=x+1, which of the following statements are true?  A: (f · g)(x)=4x^2+2x-2  B: (f · g)(x)=4x+2 C: (g · f)(x)=2x-2 D: (g · f)(x)=x 5.) If f(x)=2√x and g(x)=9x, which of the following statements is true?  A: (g · f)(x)=√18x  B: (f · g)(x)=2√3x C: (f · g)(x)=6√x D: (g · f)(x)=x

 

Answer 1

1 )  f(x)=3x+9

Let f(x)= 3x+9 = y

f(x) = y and 3x+9 = y

x = ƒ⁻¹(y) -------------> (1)

3x + 9 = y

Subtract 9 from each side

3x = y - 9

x = (y - 9) / 3 ----------->(2)

From (1) and (2)

ƒ⁻¹(y) = (y - 9) / 3

Substitute with y by x

ƒ⁻¹(x) = (x - 9) / 3

ƒ⁻¹(x) = (1/3)x - 3

The option A is the right choice

 

 

 

 

Answer 2

4)Given functions are f(x)=4x-2 and g(x)=x+1

(f · g)(x) = [(4x-2)(x+1)]

             = [(4x)(x+1) - (2)(x+1)]

             = [(4x^2+4x) - (2x+2)]

            =  [(4x^2+4x-2x-2)]

(f · g)(x)=  [(4x^2+2x-2)]

The option A is correct.

 

Answer 3

2) f(x ) = 3 / x  and g(x ) = 3x.

A: (f · g)(2)

= f(2) * g(2)

= (3/2) * 3(2)

= (3/2) * 6

= 9 

Therefore (f · g)(2) ≠  2.

B: (g· f)(2)

= g(2) * f(2)

= (3/2) * 3(2)

= 9 

Therefore   (g· f)(2) ≠ 0. 

C: (f · g)(9 )

= f(9) * g(9)

= (3/9) * 3(9)

= (1/3) * 27

= 9 

Therefore (f · g)(9) ≠  1

D: (g· f)(-9)

= g(-9) * f(9)

= (3/-9) * 3(-9)

= (-1/3) * -27

= 9 

Therefore (g· f)(-9) ≠ -1

None of them is True.

Answer 4

3) Let the inverse functions be f(x ) = x² and g(x ) = √ x.

A: f(x ) / g(x )

= x² / √ x

= x^3/2

Therefore f(x ) / g(x ) ≠  1.

Therefore the statement is False.

B: f(x )  ≟  -g(x )

x²   ≟  - √ x

x²  ≠ - √ x

Therefore f(x )  ≠  -g(x ).

Therefore the statement is False.

C: (f · g)(x )

= f(x ) * g(x )

= x² * √ x

= x^5/2 

Therefore (f · g)(x ) ≠  1.

Therefore the statement is False.

D: (g· f)(x )

= g(x ) * f(x )

= √ x * x²

= x^5/2 

Therefore (g· f)(-9) ≠ x.

Therefore the statement is False.

Answer 5

5) Let the inverse functions be f(x ) = 2√x and g(x ) = 9x.

A: (g· f)(x )

= g(x ) * f(x )

= 9x * 2√ x

= 18x^3/2 

Therefore (g· f)(x ) ≠ √18x.

Therefore the statement is False.

B: (f · g)(x )

= f(x ) * g(x )

= 2√ x * 9x

= 18x^3/2

Therefore (f · g)(x ) ≠  2√3x.

Therefore the statement is False.

C: (f · g)(x )

= f(x ) * g(x )

= 2√ x * 9x

= 18x^3/2

Therefore (f · g)(x ) ≠ 6√x.

Therefore the statement is False.

D: (g· f)(x )

= g(x ) * f(x )

= 9x * 2√ x

= 18x^3/2 

Therefore (g· f)(x ) ≠ x.

Therefore the statement is False.